Question

Consider National-Income Model: National Income: Consumption: Investment: Government Sector: Taxes: Y=C+I+G C = a + b (Y-T) I=k+rY G=GO T=f+jY <b<1 (<r<1 a>0 in mln dollars; k>O in mln dollars; Go >O in mln dollars fo in mln dollars; 0<j<1 1) Discuss in words the meaning of each of the equations in the model (3 points); 2) Find the equilibrium level of GDP (Y*) in reduced form (3 points); 3) If we know the parameters of the system, find the numerical value of the equilibrium GDP (Y*) as well as the equilibrium levels of C, I, and T (3 points); Parameters' values are as follows: a = 10; b = 0.7; f= 3; j = 0.2; k= 25; r=0.03. Endogenous Government Expenditure is Go = 55. 4) Find the government-expenditure multiplier and discuss its economic meaning (3 points); 5) Find the non-income tax multiplier and discuss its economic meaning (3 points); 6) Find the extent to which an increase in the income tax rate () will affect the equilibrium income Y (3 points). its es rare sy mein are provints)

Answer 1

1) The National income equation depicted here is for a closed economy, where all the output produced in a country is exhausted domestically. Total expenditure can be subdivided into 3 parts - Consumption (C), Investment (I) and Government spending (G).

So, in expenditure method, the national income is the sum of all three expenditure. Hence,

National Income, Y = C + I +G

Now, Consumption, C = a + b(Y -T)

Y - T = the disposable income of the consumer. This is the income that an individual can divide between consumption and saving.

now, as we see that, T = f + jY

Government has imposed a two part tax. One part is lump-sum and the amount of this tax is f . The other part of the tax is proportional i.e, it is dependent on Y. Here, if income is increased by 1 unit, tax will increase by j.

$\Delta T/\Delta Y$= j

So, the disposable income is, Y - T = Y - f - jY = -f +(1-j)Y

so Consumption, C = a + b(Y- T) = a+ b[-f+(1-j)Y]

or, C = a - bf + b(1-j)Y

$\Delta C/\Delta (Y-T)$= b

this is the MPC or marginal propensity to consume of the consumer. This means if the disposable income is increased by 1 unit then the consumption will increase by b unit.

Now putting T = Y - f - jY,

$\Delta C/\Delta Y$= b(1-j)

This means if the income is increased by 1 unit then the consumption will increase by b(1-j) unit.

The rest of the part of the consumption expresses the autonomous consumption.

Investment is also divided into two part.

I = k +rY

K = autonomous investment

r = MPI = marginal propensity to invest

This means if the income is increased by one unit then investment will increase by r unit

$\Delta I/\Delta Y$= r

Government spending is autonomous and is equal to G_0.

Y = C+I+G of, y = a + b (Y-T) + K+2y + Go. ar y = a + b (y-f-j4) +ktry+ Go. or, ya a bft6(1-1) Y + k + 20y + Go. on y-6(1-j) Y-py = a-bf + k + Go. cu 1-661-4) -r] y = a -68 +k+Go. er, y , a-oftk tgo. where, y - - b(1-j)-8. equilibrium tersel of GDP 1 3) tutting putting the values in the the equilibrium level of GDP, Y, we gel .. ya 10 - 0'7 X 3+25+ 55 1- 097(1-02) -0.03 10 - 2'1 +80. 1- 0'56 - 0'03 90-21. 1-0'59 87-9 - - 21439 0:41. ya. 2,14'39 min dollars The t+jy 3 + 0'x 214'39 3+ 42'878 = 45.878 T* 45.878 min dollars. ez a +b(y-7) - 10+ 0'7(214'39 - 45'878) Z. 10 +0'7X 168'512 - 10+117.9584 * = 127.9584 men dollars. = 1279584 I = K + yo y = 25+ 0.03 X 214'39 - 25+ 6'4317 = 31' 4317 T* 31.4317 min dollars

the a government expenditure is increased by let Now, the NI equation is , ya a+b (Y-T) tk toy't Got AG or, y'= a bf to (1-j)Y'tki ny't Got AG or (1-6 (1-3)=80) y'e a bf tk + Go + AG or y a-bftwt Go + AG 1-b(1-j) - 2 as y a-b a-bftk + Go 1-6 (1-j) -2 - AG 1-6(1-5)=20 or y = yx + -nho 49. [yta equilibrium level of GDP when G = Go] o'cy* AG - 1-6 (1-j)-2 or DY AG l-b(1-1)-r AY 1-6 (1-j)-p. This shows the change = Government expenditure multiplier . in y due to per unit change in G. the values of the paramelers. putting A - 0761-09) -0'03 1-07x0'8-0'03 - 056 -0'03 - 059 This means that per unit change es G will change Y by 2 041, = 2.439 crounded to 3 decinal . Places) 4 39 unit